{"product_id":"modularity-and-generalized-fermats-equation","title":"Modularity and Generalized Fermat's Equation","description":"This volume contains the detailed exposition of virtual lectures on the theme \"\"Modularity and Generalized Fermat's Equation\"\", which were delivered in January-April 2022 during the program organized by the Bhaskaracharya Pratishthan Research Institute in Mathematics, Pune, India. Modularity of elliptic curves over the field of rational numbers plays a central role in the proof of the celebrated Fermat's Last Theorem (FLT) by Wiles and Taylor-Wiles in 1995. Around the same time Henri Darmon and his collaborators initiated the study of Generalized Fermat Equations (GFE) in a series of papers. This work leads to an ambitious program to study the generalized Fermat equation $aX^m bY^n=cZ^r$ using the modularity of abelian varieties of $\\mathrm{GL}_2$-type over totally real fields. This volume covers some of the background material and presents the current state of the art in this area.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":58639711568207,"sku":"9781470485535","price":197.95,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0061\/0372\/8217\/files\/9781470485535_1-modularity-and-generalized-fermats-equation.jpg?v=1788325812","url":"https:\/\/www.suomalainen.com\/products\/modularity-and-generalized-fermats-equation","provider":"Suomalainen.com","version":"1.0","type":"link"}